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A195294 Smallest palindromic prime containing the n-th palindrome as central digit(s), or 0 if no such prime exists. 1
101, 313, 2, 3, 11411, 5, 10601, 7, 181, 191, 11, 0, 0, 0, 0, 0, 0, 0, 0, 101, 1311131, 1212121, 131, 11411, 151, 1616161, 1117111, 181, 191, 1120211, 1221221, 72227, 32323, 12421, 3425243, 1126211, 12721, 12821, 1129211, 73037, 313, 73237, 13331, 1134311, 353 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..11000

G. L. Honaker, Jr. & C. K. Caldwell, Palindromic Prime Pyramids, p. 1.

G. L. Honaker, Jr. & C. K. Caldwell, Supplement to "Palindromic Prime Pyramids"

Eric Weisstein's World of Mathematics, Palindromic Number

Eric Weisstein's World of Mathematics, Palindromic Prime

Index entries for sequences related to palindromes

EXAMPLE

a(5) = 11411 because A002113(5) = 4 and 4, 141, 343, 737, 939, and 10401 are all composite, but 11411 is prime.

a(12) = 0 because A002113(12) = 22 and every palindrome with 22 in the center (22, 1221, 2222, ...) has an even number of digits, so is divisible by 11.

MATHEMATICA

lst1 = {}; lst2 = {}; r = 353; Do[d = IntegerDigits[n, 10]; If[Reverse[d] == d, AppendTo[lst1, n]], {n, r}]; Do[a = lst1[[p]]; If[EvenQ@IntegerLength[a] && ! PrimeQ[a], AppendTo[lst2, 0], If[PrimeQ[a], b = a, n = 1; While[True, b = FromDigits[Join[Flatten@IntegerDigits@PadLeft[{a}, 2, n], Reverse@IntegerDigits[n]]]; If[PrimeQ[b], Break[]]; n++]]; AppendTo[lst2, b]], {p, Count[lst1, _Integer]}]; Prepend[lst2, 101] (* Arkadiusz Wesolowski, Jan 29 2012 *)

CROSSREFS

Supersequence of A002385 (palindromic primes).

Sequence in context: A033241 A140021 A139701 * A142578 A256048 A252942

Adjacent sequences:  A195291 A195292 A195293 * A195295 A195296 A195297

KEYWORD

base,nonn

AUTHOR

Arkadiusz Wesolowski, Sep 14 2011

STATUS

approved

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Last modified August 9 01:35 EDT 2020. Contains 336310 sequences. (Running on oeis4.)